Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4×C13⋊C3 | C2 | semidirect |
| 3. C4⋊C4×C13⋊C3 | C2 | semidirect |
| 4. C22⋊C4×C13⋊C3 | C2 | semidirect |
| 5. C42×C13⋊C3 | C2 | semidirect |
| 6. C4×D4×C13 | C3 | semidirect |
| 8. D4×C13⋊C3 | C4 | direct (N × H) |
| 15. C22×C4×C13 | C2×C3 | semidirect |
| 16. C13×C4⋊C4 | C2×C3 | semidirect |
| 17. C13×C22⋊C4 | C2×C3 | semidirect |
| 18. C42×C13 | C2×C3 | semidirect |
| 21. C22×C13⋊C3 | C2×C4 | semidirect |
| 25. C4×C13⋊C3 | C2×C4 | semidirect |
| 26. C4×C13⋊C3 | D4 | direct (N × H) |
| 28. D4×C13 | C3×C4 | semidirect |
| 41. C22×C13 | C2×C3×C4 | semidirect |
| 45. C4×C13 | C2×C3×C4 | semidirect |
| 46. C4×C13 | C3×D4 | semidirect |
| 52. C13⋊C3 | C4×D4 | direct (N × H) |
| 53. C4×D4 | C13⋊C3 | direct (N × H) |
| 66. C22×C4 | C2×C13⋊C3 | semidirect |
| 67. C4⋊C4 | C2×C13⋊C3 | semidirect |
| 68. C22⋊C4 | C2×C13⋊C3 | semidirect |
| 69. C42 | C2×C13⋊C3 | semidirect |
| 70. C13 | C3×C4×D4 | semidirect |
| 80. D4 | C4×C13⋊C3 | direct (N × H) |
| 92. C22 | C2×C4×C13⋊C3 | semidirect |
| 96. C4 | C2×C4×C13⋊C3 | semidirect |
| 97. C4 | D4×C13⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C13⋊C3 | 2 |
| C22×C4×C13⋊C3 | 2 |
| C4⋊C4×C13⋊C3 | 2 |
| C22⋊C4×C13⋊C3 | 2 |
| C42×C13⋊C3 | 2 |
| C4×D4×C13 | 3 |
| C3×C4×D4 | 13 |